Mayor Giuliani’s “art war” against the Brooklyn Museum has hurt his popularity – but he’s still leading would-be Senate rival Hillary Clinton, a new poll shows.

Asked whom they would vote for now, 46 percent of New Yorkers said they’d pick Giuliani, while 42 percent said they’d choose the first lady, the Marist College poll found.

That’s a 3-point drop for Giuliani from last month, before the battle erupted over the incendiary “Sensation” exhibit.

A majority of the 702 registered voters surveyed said the museum flap was responsible for changing their opinion of Giuliani – with 30 percent saying it gave them a worse opinion of the mayor, and 21 percent saying it improved their opinion. Forty-nine percent said their opinion was unchanged.

And 59 percent of the respondents sided with Clinton’s opinion that the exhibit is offensive but it’s wrong to cut off museum funding.

Giuliani is outraged by a painting of the Virgin Mary that includes clumps of elephant dung and cutouts from pornographic magazines. He has called the piece “sick stuff” and stopped all city funding to the museum, which is suing to have it restored.

Clinton has said she finds the exhibit offensive, but would not cancel its government funding.

The poll, which has a margin of error of 4 percentage points, was released on the eve of a courtroom confrontation over the issue.